This invention relates to electronic musical instruments or synthesizers and more particularly relates to such apparatus which stores a digital representation of a waveshape.
Electronic musical instruments are capable of producing audible musical notes from either analog or digital circuitry. The digital approach to sound production was described by Max V. Matthews in a paper entitled "An Acoustic Compiler For Music And Psychological Stimuli" published in the May, 1961 issue of The Bell Systems Technical Journal. Mathews describes the basic concept of storing a digital representation of a wave-shape and repetitiously reading the waveshape from the representation at a predetermined rate in order to produce a musical note.
The Mathews concept has been used in a variety of electronic musical instruments. For example, one adaptation of the concept used in connection with electronic organs is described in U.S. Pat. No. 3,515,792 (Deutsch-June 2, 1970). Both Mathews and Deutsch teach the concept of digitally representing the amplitude of a sound waveshape at a plurality of points representing arbitrary angles of the waveshape. The waveshape is then sampled at a variety of frequencies depending on the notes to be produced. Although the Deutsch and Mathews systems both result in usable sounds, they fail to take into account the alias distortion created when the digital amplitudes are stored at arbitrary phase angles and sampled at unrestricted frequencies. This alias distortion results from alias frequencies which are an unavoidable consequence of the act of sampling or desampling a signal, such as a stored wave-shape. Alias distortion is potentially intolerable: (a) if the alias frequency components occur within the low-passband of the output of a system due to sampling at too low a rate; (b) if the magnitudes of the alias frequency components are "too great"; (c) or, for musical purposes, if the alias frequency components move in a frequency direction opposed to the direction of the fundamental frequency of a note (e.g., an alias frequency moves lower in pitch as a desired fundamental note moves higher in pitch). Alias distortion also results from the inability of a digital number of finite length to represent an analog quantity with 100 percent precision. Accuracy improves as the length of the digital number increases, but in general, some small error remains. Although alias distortion is always present in a sampled signal, it has been discovered that the effect of the distortion in numerical systems can be minimized by sampling at 2.sup.N times the desired fundamental frequency. The 2.sup.N harmonically sampled signal will have alias products which occur at frequencies which are integer multiples of the fundamental. This means that if there were energy present at one of these harmonics in the desired wave, the effect of the aliased energy would likely go unnoticed by a human observer because it would be merely an augmentation or diminution of that desired harmonic's energy and would merely slightly change the timbre of the wave produced. If the frequency of the desired fundamental were changed, the alias products would move in the same direction, and, harmonically, there would always be less chance of their being noticed by a human listener. If a signal is sampled at other than 2.sup.N times the fundamental, the alias components, in general, do not occur in integer multiples of the fundamental. This non-harmonic type of alias distortion is easier for a human ear to detect than harmonic type alias distortion due to psychoacoustic phenomena involving differential perceptions.
More specifically, it has been discovered that sound waves can be produced with improved fidelity and alias distortion can be minimized by sampling a stored waveshape only at a rate 2.sup.N times the fundamental frequency of the note desired, where N is an integer which is varied to achieve control of the octave of the desired output wave. Likewise, the synthesis of a waveshape is improved by storing a digital representation of the amplitude of the waveshape at a plurality of phase angles, each phase angle being at (2.pi.X)/2.sup.K radians, where X and K are integers. These two techniques also can be combined in order to more faithfully reproduce the waveshape stored in a digital manner.